Techniques of Teaching Mathematics

I taught private tuition in Mathematics to students junior than me while I was studying in secondary school. Over time, I came to become aware of some skills in handling some special situations during the lessons. Here are things you may say in class under certain circumstances:

. You don't want to go through all the possible cases. You just show one, and let the student figure out the rest,

"Without loss of generality, .......... "

. You know it's true, but you've lost your notes and you don't know how to prove it,

"It is obvious that .......... "

. You are struggling on how to explain, and your student suddenly reminds you the critical point,

"It now becomes clear that .......... "

. You feel tired after a long day's study yourself, and you don't want to explain in details,

"This is trivial."

. You are desperate to go on Friday afternoon,

"The rest are left as exercises to students."